Hangyu Liu(Roger)

What is quantization of charge? Millikan oil drop experiment and equipment setup The data collection and analysis The conclusion

In general, the quantization of charge is the principle that the charge of any object is an integer multiple of the elementary charge. For example: 0e, 1e, -1e Yes 0.5e, ½e, -0.9e No

In 1909, R. Millikan reported a reliable method for measuring ionic charge. The main process is to observe the motion of small oil droplets under the influence of an electric field. It involves three types of motion: gravity fall motion (g); electric field aided downward motion (d); electric field aided upward motion (u).

Webcam Viewing Scope Atomizer Droplet Viewing Chamber LED Light Source Platform Plate Charging Switch Stopwatch Gadwin PrtSc Constant Velocity

TypeTop Plate Voltage Y 1 (minor lines) Y 2 (minor lines) T1T1 T2T2 g/ : :48.77 d :30.041:35.72 u :57.251:58.49 The black lines: gravity fall motion (g) The red lines: electric field aided downward motion (d) The blue lines: electric field aided upward motion (u).

Figure: free body diagrams of all three cases. Thus, for gravity fall measurements (f): F g =mg=4/3*πr 3 ρg F d= 6πη eff rv η eff= η*[1/(1+b/pr)] due to Stokes’ law F d =F g, 4/3*πr 3 ρg=6πη eff rv, we can find For electric field aided upward motion (u): F E = F d + F g, q=(F d +F g) /E=[6πη eff rv+4/3* πr 3 ρg]*s/V For electric field aided downward motion (d): F E = F d - F g, q=(F d -F g) /E=[6πη eff rv-4/3* πr 3 ρg]*s/V The definitions of symbols used: q - charge carried by the droplet s – separation of the plates ρ – density of oil g – acceleration of gravity η eff - viscosity of air r – the radius of drop v – the velocity of drop V – potential difference across the plates in b – constant, equal to 8.13* N/m

In general, in order to figure out the uncertainty of data, we could measure the same thing for several times. While in this particular case, we have an upward motion and a downward motion for a same charge, so we just need to get the different values for the same charge and calculate the average difference between them as the uncertainty.

By adjusting the scaling, I found out the value of charge is ( )* , which is smaller than the expected value 1.6* However, we clearly see the evidence of quantization of charge, so it might be experimental error which I can not figure out.